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Thread: Diminishing Returns - Avoidance

  1. #1
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    Diminishing Returns - Avoidance

    Thanks and credit to Whitetooth for doing all the math and analysis to get us the numbers and formula that make all of this explanation possible. (Want math? It's in post #2)

    Dodge, parry, and miss are subject to diminishing returns. When you determine how much dodge/parry/miss you gain from rating or defense, it must be converted into the diminished amount. The diminished amount is what is added to your dodge/parry/miss chance.

    Diminishing returns on avoidance do not work like diminishing returns on stuns! There's a common belief that if you avoid an attack, your chance to avoid subsequent attacks is reduced. This is not true - read on!

    What are diminishing returns? One definition puts it this way: The principle that further inputs into a system produce ever lower increases in outputs. Basically, you get less avoidance for every point of rating than you got for the last one. There's a simple step-by-step "here's how it works" explanation of diminishing returns here: http://www.tankspot.com/forums/f63/4...ns-armour.html.

    Some things worth noting:
    • Chill of the Throne is applied after diminishing returns. If you get all buffed up outside of ICC to, say, 26% dodge, when you zone in you will have 6% dodge.
    • The diminishing returns on dodge, parry, and chance to be missed are independent of each other. Each has its own cap and formula.
    • There is no "avoidance cap". If you can get to 10% miss + 20% parry + 70% dodge, you would indeed be completely unhittable by an equal level attacker
    • Avoidance contributed by defense is subject to diminishing returns, as will be shown below
    • Your base (naked) avoidance and avoidance given by talents and racials is NOT subject to diminishing returns, and are not included in the formulas. Just add them on at the end.
    • The cap for miss has been verified for warriors only at this time.
    • The dodge and parry numbers shown on your character sheet do have diminishing returns taken into account (see Post #86 for how that works)
    • The miss chance on the defense tooltip does not have diminishing returns taken into account (see below for how to calculate miss chance.) The tooltip is also reporting only the non-diminished amount of miss chance that your defense is contributing - it does not include the basic 5% miss chance that an equal level opponent will have against you.
    • Block chance is not subject to diminishing returns at all

    The total change in an avoidance type (i.e. dodge, parry, or miss) from all sources (rating, defense, agility, etc.) must be calculated together so that the result correctly takes the diminishing returns into account. When considering an item and whether it is an upgrade or not, a total recalculation of each avoidance type using the new item's stats and all stats from other items, buffs, etc. must be performed. To avoid a great deal of tedious calculation and recalculation, an addon like Whitetooth's RatingBuster is highly recommended. RatingBuster will do the complete recalculation for a given item, and display the correct increase or decrease in stats in the item's tooltip. Get RatingBuster: WoWInterface, Curse

    Here's a sampling of rating vs. avoidance (pretty graphs are below in other posts).
    - We start at zero and just show values for different amounts of rating.
    - The expected value for each of dodge, parry and miss is simply the amount of rating divided by the rating needed for 1% (what you would have gotten as a tank in the Burning Crusade era)
    - The diminished value for each is what you will actually get.
    - See post #2 to see how these diminished numbers are actaully calculated, if you care.

    Code:
              expected  diminished    expected  diminished    expected  diminished
    rating       dodge       dodge       parry       parry        miss        miss
         0        0.00        0.00        0.00        0.00        0.00        0.00
       100        2.21        2.25        2.21        2.20        0.81        0.81
       200        4.42        4.39        4.42        4.21        1.63        1.54
       300        6.63        6.43        6.63        6.04        2.44        2.20
       400        8.84        8.37        8.84        7.73        3.25        2.81
       500       11.05       10.22       11.05        9.28        4.07        3.36
       600       13.26       11.98       13.26       10.71        4.88        3.87
       700       15.47       13.67       15.47       12.04        5.69        4.34
       800       17.68       15.29       17.68       13.27        6.51        4.77
       900       19.89       16.83       19.89       14.42        7.32        5.18
      1000       22.10       18.31       22.10       15.50        8.13        5.55
      1100       24.31       19.73       24.31       16.50        8.95        5.90
      1200       26.52       21.10       26.52       17.44        9.76        6.23
      1300       28.73       22.41       28.73       18.33       10.57        6.54
      1400       30.94       23.67       30.94       19.17       11.39        6.83
      1500       33.15       24.88       33.15       19.95       12.20        7.10
      1600       35.36       26.05       35.36       20.70       13.01        7.35
      1700       37.57       27.18       37.57       21.40       13.83        7.60
      1800       39.78       28.26       39.78       22.07       14.64        7.82
      1900       41.99       29.31       41.99       22.71       15.45        8.04
      2000       44.20       30.32       44.20       23.31       16.27        8.25
     10000      220.99       63.80      220.99       39.06       81.33       13.47
    Note that actual avoidance approaches the cap asymptotically as expected. Stacking rating to try and hit the cap will leave you disappointed. All of the above numbers are based on just the ratings. To these you need to add your base chance to dodge, parry, and be missed (don't forget an extra 2% if you're a Night Elf).

    How much rating?
    The most popular question: How much should you get then, and in what balance? Thanks to a bunch of work by Xenix, Jere, Theck and others (see here), we have some general rules for the post-3.2 world:

    Warriors and Paladins
    Take your total values for dodge and parry from the character sheet. From there, your optimal balance between dodge rating and parry rating is
    Code:
    (character_sheet_dodge-10%)/(character_sheet_parry-10%) = 1.88
    Of course, if you're outside of your "optimal balance" and you add a parry gem, that may be enough to tip the balance back. The odds of you needing to actively pursue parry are pretty low.

    Death Knights
    The parry you get converted from strength is subject to diminishing returns. This means you will always have lots of parry rating. Your optimal balance is
    Code:
    dodge is always better
    Frequently Asked Questions

    Q What about parry gems?
    A If you're a Death Knight, you're never using them. For a Paladin or Warrior, it may be that a parry gem may satisfy the optimal balance for you. Then again, most will only use such a gem to satisfy meta requirements (the greater debate of stamina vs. avoidance gems is not something we'll go into here), so the likelihood of having the "wrong" gem socketed and making a big difference is basically none. As noted, the likelihood that you will need to stack parry gems to achieve your "optimal balance" is pretty low. Even if you did need multiples, the change in your overall avoidance is on the order of fractions of a percentage.

    Q Does gear that is itemised with parry suck?
    A Nope. The parry you get from itemisation will help keep you in balance as you go. Of course, the old comparisons still apply: if you have iLevel 187 bracers with 20 dodge rating and get iLevel 200 bracers with 55 parry rating, that's an upgrade no matter how you look at it. If you have bracers with 50 dodge rating and get bracers with 55 parry rating, it's a little less clear as to whether that's an upgrade.

    Q Does this mean that every X avoidance you add increases time to live linearly, like armour?
    A Nope, it falls out differently for avoidance. Being based on probabilities, you can't determine a concrete amount of time to live it would give anyway.

    Q Are we sure that chance to be missed subject is to diminishing returns?
    A Yes. Daelo told us so on the WoW forums. Whitetooth has done an insane amount of testing to determine what the miss cap is (here: The Miss Cap)

    Q Has anyone confirmed the miss cap for Paladins, Deathknights, or Druids yet?
    A Not 100% absolutely yet, but it's a good bet the cap is the same as Warriors for Paladins and Deathknights since the dodge and parry caps are the same. Druids may have a different cap given their cap for dodge is different from everyone else's.

    Q What's my chance to be missed at 540 defense?
    A 9.29% unless you're a Night Elf, in which case it's 11.29%. Example 3, below, breaks down the math for 540 defense (689 defense rating from gear)

    QIs the dodge and parry chance listed on the character panel before or after diminishing returns?
    AThe dodge and parry percentages have diminishing returns taken into account. It's a bady worded tooltip for sure. See here: Post #86

    Q What's the macro for avoidance now?
    A http://www.tankspot.com/forums/f120/...ce-macros.html

    Q Is there a real example of the calculation I can see?
    A These use Patch 3.1 values: Warrior and Death Knight. The method used there is the same as you'll use with the current values, though.
    Last edited by Satrina; 01-16-2010 at 01:13 AM.

  2. #2
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    Here comes the math
    The basic conversions for defense, dodge and parry rating at level 80 are:
    Code:
     4.91850 defense rating  = 1 defense skill
    45.25019 dodge rating = 1% dodge chance
    45.25019 parry rating = 1% parry chance
    122.9625 defense rating = 1% dodge/parry/miss chance
    
    These values are correct as of patch 3.2
    You generally only gain miss chance from defense, though things like the Night Elf racial (which is not subject to diminishing returns) are around. Testing to determine the exact diminishing returns on miss has not been completed. We know that miss is subject to diminishing returns because of Daelo's comment here: WotLK Beta (US-English) Forums -> Avoidance change. (emphasis mine)

    Quote Originally Posted by Daelo
    We just restarted the servers to fix an issue with the diminishing returns formula we added for Dodge, Parry, and the enemy's chance to miss you.
    Whitetooth has also done the work to isolate the miss cap (link above)

    There is a coefficient (k) for each class that bounds the diminishing returns:
    Code:
    Class             k
    Warrior		0.956
    Paladin		0.956
    Deathknight	0.956
    Druid		0.972
    
    These values are correct as of patch 3.2
    There is a cap (c) for each class, for each avoidance type:
    Code:
    Class		type	c		1/c  
    Warrior		Dodge	88.129021	0.011347
    Warrior		Parry	47.003525	0.021275
    Warrior         Miss    16              0.0625
    Paladin		Dodge	88.129021	0.011347
    Paladin		Parry	47.003525	0.021275
    Paladin         Miss    16              0.0625       (presumed since all other caps are the same as warriors)
    Deathknight	Dodge	88.129021	0.011347
    Deathknight	Parry	47.003525	0.021275
    Deathknight     Miss    16              0.0625       (presumed since all other caps are the same as warriors)
    Druid		Dodge	116.890707	0.008555
    
    These values are correct as of patch 3.2
    Finally, the agility you have beyond your naked agility also affects your dodge chance, based on class:

    Code:
    Class          Dodge/Agility
    Warrior		0.0118
    Paladin		0.0167
    Deathknight	0.0118
    Druid		0.0209
    
    These values are correct as of patch 3.2
    Note that your base (naked) avoidance and avoidance given by talents and racials is NOT subject to diminishing returns - do not include them in the calculation

    Also note that your base defense (what you have when you're naked) is not used in calculations - only the defense you gain from gear.

    The net amount of avoidance you get is given by:



    Where
    A is the amount of avoidance before diminishing returns
    c is the cap for the avoidance stat
    k is the constant for your class
    Ad is the amount of avoidance after diminishing returns are applied (how much your avoidance actually increases)

    Each avoidance type (dodge, parry) is calculated separately from the other. The amount of dodge you have does not affect the diminishing returns on your parry, and vice-versa.

    Example 1 - Dodge

    Suppose a warrior has 5% dodge when naked with +261 agility from gear, +557 defense on gear, and +368 dodge rating on gear:

    First, calculate the base dodge chance from gear:
    1a) Convert defense rating to defense skill: 557/4.9185 = 113 defense skill
    1b) Convert defense skill to base dodge chance: 113 * 0.04 = 4.52%
    1c) Convert dodge rating to base dodge chance: 368/45.25019 = 8.13256%
    1d) Convert agility to base dodge chance: 261 * 0.01360 = 3.5496%
    2) Calculate k/A: 0.956/(4.52 + 8.13256 + 3.5496) = 0.059
    3) Calculate 1/c + k/A: 0.01135 + 0.059 = 0.07035
    4) invert the result from step 3: 1/0.07035 = 14.21434%. This is Ad, the diminished amount of dodge actually gained

    Now add the diminished dodge from gear to the dodge when naked, and the warrior will end up with 5% + 14.21% = 19.21% dodge

    Example 2 - Parry

    Suppose a deathknight has 5% parry when naked with +255 defense rating on gear, and +375 parry rating on gear:

    First, calculate the base parry chance from gear:
    1a) Convert defense rating to defense skill: 255/4.9185 = 51 defense skill
    1b) Convert defense skill to base parry chance: 51 * 0.04 = 2.04%
    1c) Convert parry rating to base parry chance: 375/45.25019 = 8.28726%
    2) Calculate k/A: 0.956/(2.04 + 8.28726) = 0.09257
    3) Calculate 1/c + k/A: 0.02128 + 0.09257 = 0.11385
    4) invert the result from step 3: 1/0.11385 = 8.78383%. This is Ad, the diminished amount of parry actually gained

    Now add the diminished parry chance to the base parry chance and the deathknight will end up with 5% + 8.78% = 13.78% parry

    Example 3 - Miss
    We know that each point of defense skill increases your chance to be missed by 0.04%, and that defense is currently the only way to increase your chance to be missed. Suppose a human warrior has +689 defense on gear:

    1a) Convert defense rating to defense skill: 689/49.18499 = 140 defense skill
    1b) Convert defense skill to base miss chance: 140 * 0.04 = 5.6%
    2) Calculate k/A: 0.956/5.6 = 0.17071
    3) Calculate 1/c + k/A: 0.0625 + 0.17071 = 0.23321
    4) invert the result from step 3: 1/0.23321 = 4.2879%. This is Ad, the diminished amount of miss actually gained

    The warrior will end up with 5% + 4.29% = 9.29% miss. If the warrior were a Night Elf, the chance to be missed would be 11.29% (because of the Quickness racial.)

    You can not simply calculate what a given item "should" increase your stats by and just add it to what you have.

    Example 4 - Optimum Balance vs. Stamina
    Suppose we have a warrior with 695 defense rating, 600 dodge rating, and 100 parry rating.
    This comes out to 26.61% dodge and 18.21% parry. Following the opimum balance formula, we see that the warrior has (26.61 - 10)/(18.21 - 10) = 2.02

    If the warrior trades one stamina gem for +20 parry rating, then the 695/600/120 stats become avoidances of 26.61% and 18.67%, for a ratio of 1.92. Trading another stamina gem for 20 more parry, then the 695/600/140 stats become 26.61% and 19.14%, for a ratio of 1.82. In this case two parry gems brings the warrior back into optimal balance at a cost of 60 stamina.

    Example 5 - Trading for Optimum Balance
    Suppose we have a warrior with 695 defense rating, 600 dodge rating, and 100 parry rating.
    This comes out to 26.61% dodge and 18.21% parry. Following the opimum balance formula, we see that the warrior has (26.61 - 10)/(18.21 - 10) = 2.02

    If the warrior trades one dodge gem for a parry gem then the 695/580/120 stats become avoidances of 26.30% and 18.67%, for a ratio of 1.88. In this case changing one dodge gem for a parry gem brings the warrior back into optimal balance.

    Example 6 - Optimum Balance vs. Defense
    Suppose we have a warrior with 695 defense rating, 600 dodge rating, and 100 parry rating.
    This comes out to 26.61% dodge and 18.21% parry. Following the opimum balance formula, we see that the warrior has (26.61 - 10)/(18.21 - 10) = 2.02

    If the warrior trades one dodge gem for defense rating, then the 695/580/100 stats become avoidances of 26.41% and 18.38%, for a ratio of 1.96. Ultimately, three defense gems would be required to bring the ratio below 1.88 if trading dodge gems for them.

    If the warrior were to trade stamina gems for defense gems then a trade of 6 gems would be required to bring the ratio below 1.88, or 180 stamina for 120 defense.
    Last edited by Satrina; 01-16-2010 at 01:14 AM.

  3. #3
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    But how do we know that avoidance-talents are not diminished. With high avoidance on gear speccing in and out of the talents would show it, anyone done this yet?

    edit: nwm, whitetooth had alrdy tried it
    Last edited by weel; 10-23-2008 at 02:03 AM.

  4. #4
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    Does increased dodge rating give diminishing returns on parry? Or are the two stats evaluated independently?

  5. #5
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    evaluated differently, look at his examples.

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  6. #6
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    That's what I thought, it's just these couple sentences that made me think it might be otherwise:

    The total change in avoidance from all sources (rating, defense, agility, etc.) must be calculated together so that the result correctly takes the diminishing returns into account. When considering an item and whether it is an upgrade or not, a total recalculation of avoidance using the new item's stats and all stats from other items, buffs, etc. must be performed.

  7. #7
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    Clarified in the text.

  8. #8

    Some Druid Graphs

    I did a little Excel for Druid Agility to Dodge conversions @ 80






    Here are my Sets using Whitetooths Formula



    *Edit*
    These numbers do not include the base Dodge from Agi or Talents

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    Nice work pig .

  10. #10
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    Charts are hot.

    Also, the TankPoints addon is another addon that seems to work well for this sort of thing, and is very easy to use. You can bring up an extensive calculator and adjust your stats as required, with all the outputs calculating automatically. It also puts a +/- value for each item in the popup info box that compares it to whatever item you have equiped for that slot.
    Tankity spankity.

  11. #11
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    Thank you.

    Made an Exel file for my self using this info and expended it with the 0.25 parry rating DK's get from 1 str. I only insert the ratings I have ( def rating, parry rating block rating, agility, strength ) and it gives me 12 outcomes. Those are 3 for each of the 4 tanking classes. Each class has an outcome fore Undeminished Dodge+Parry+Baseavoidance, the same for Deminished and 1 wich also includes Block and Chance to be missed. I putted block in it in a way it didn't get deminished cause this new mechanics only work for parry and dodge.

    Anyway, thanks for the easy explanations. I wish I could post my Exel file here but it is either not posile or I don't know how to do it.

    Anyway, thanks for your topic.

  12. #12
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    Click "Post Reply" & scroll down where it says "Additional Options." There is a button which says "Manage Attachments," click that. Should be able to upload your excel file so we can see your work.

  13. #13
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    I hope it works. Anyway, The fields in which you can put in your own variables is colored yellow and the fields which show the results are colored orange to make it easier for you to use. I did that because I wanted to keep it simple first and the kept expanding it so it grew in an odd shape. But it funcions perfecly since i got the same answers when I entered the values from the shown examples.

    If you see any of my mistakes, just send me a PM or just reply to this topic.

    Hope it helps you a bit.
    Attached Files

  14. #14
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    first, thanks for all of your hard work that you put into this.
    second, i am stupid and need clarification

    the talents that increase dodge and parry, are they good because they are NOT affected by diminishing returns?

    also are these diminishing returns a huge deal? if i had 5% would i lose 1%, or is it more towards 5% goes down by 0.1%?

  15. #15
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    Talents such as Anticipation & Deflection are good because they are not affected by diminishing returns (same with racials). Baseline stats are unaffected. Period.

    If you're looking for more information, have a look at this thread.
    Last edited by Arideni; 11-06-2008 at 09:41 AM.

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    RatingsBuster has to be one of the greatest and most important mods ive ever used.
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    First off, thanks for the very informational post

    After reading and thinking about it a bit, do however still have a few questions...
    It basically comes down to: how will this affect us when choosing gear?

    From what I understand is that the diminishing returns for avoidance now work quite similar to the diminishing returns of armor.
    By this I mean that a point of dodge rating will yield less dodge percentage the more you add, but that every point of dodge rating will have a linear decrease in the amount of damage received (on average over time).

    The tricky part is that unlike armor, avoidance is distributed over three different stats (dodge, parry & miss/defense).
    Assuming the comparison with diminishing returns from armor is correct, the best way to get maximum time-to-live from your avoidance stats would be to keep them as balanced as possible. Increasing dodge while you already have more dodge than parry, will yield less benefit than adding the same amount parry.

    I'm thinking of the following gearing rules:
    • If you have more dodge than parry, go for parry gear.
    • If you have more parry than dodge, go for dodge gear.
    • Defense gear is always good, but don't favor defense over dodge or parry when you're lacking one of those.

    Any feedback would greatly be appreciated, and please do correct me if I'm wrong.
    Right now I'm trying to find some easy guidelines that prevent me from grabbing a calculator/addon each time some gear choice has to be made

  18. #18
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    the first 2 rules you state make some sense, but defense is likewise almost as good as dodge point for point even without diminishing returns. I'd say that defense is probably a better stat to stack than parry most of the time because you get more return out of it, it gives you the best avoidance ever (miss) and it also gives you some parry, AND some shield block rating which is a good way to increase your overall mitigation by ensuring more attacks get blocked. it's the easiest stat to balance yourself around, but dodge converts at a slighty better rating so it's prioritized a little higher.

    I'd just go with Xav's advice and just go pure defense because you'll be hurting to stay uncrittable anyways =P

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    I'm not sure if I'm correct but I was thinking of gemming for parry in red sockets as blue level 80 gear seems dodge heavy, but having done a closer read of this thread, am I right when I say that because of the relative caps on dodge and parry, its only worth gemming for parry if the bit of your dodge thats subject to diminishing returns is somewhere in the region of twice the part of your parry thats subject to diminishing returns?

    That was probably badly explained, but presumably the lower cap on parry means the diminishing returns curve is far steeper than for dodge?
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  20. #20
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    aha! thanks kazey
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